已知{log2an}为等比数列,且满足log2a1+log2a2+...log2a12=12,则a6*a7=
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已知{log2an}为等比数列,且满足log2a1+log2a2+...log2a12=12,则a6*a7=
![已知{log2an}为等比数列,且满足log2a1+log2a2+...log2a12=12,则a6*a7=](/uploads/image/z/20067991-7-1.jpg?t=%E5%B7%B2%E7%9F%A5%7Blog2an%7D%E4%B8%BA%E7%AD%89%E6%AF%94%E6%95%B0%E5%88%97%2C%E4%B8%94%E6%BB%A1%E8%B6%B3log2a1%2Blog2a2%2B...log2a12%3D12%2C%E5%88%99a6%2Aa7%3D)
/>log2a1+log2a2+...log2a12=12
∴ log2 (a1*a2*.a12)=12,且a1,a2,.a12都是正数
a1*a2*a3*.a12=2^12
∵a1*a12=a2*a11=a3*a10=a4*a9=a5*a8=a6*a7
∴ (a6*a7)^6=2^12
∴ a6*a7=2^2=4
∴ log2 (a1*a2*.a12)=12,且a1,a2,.a12都是正数
a1*a2*a3*.a12=2^12
∵a1*a12=a2*a11=a3*a10=a4*a9=a5*a8=a6*a7
∴ (a6*a7)^6=2^12
∴ a6*a7=2^2=4
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